Subregion generalized variational principles for elastic thick plates

Tn this paper, the subregion generalized variational principle for elastic thick plates is proposed. Its main points may be stated as follows:1. Each subregion may be assigned arbitrarily as a potential region or complementary region. The subregion variational principles of potential energy, complementary energy and mixed energy represent three special forms of this principle.2. The number of independent variational variables in each sub-region may be assigned arbitrarily. Any one of the subregions may be assigned as a one-variable-region, two-variable-region or three-variable-region.3. The conjunction conditions of displacements and stresses on each interline of neighbouring subregions may be relaxed. On the basis of this principle the finite element analysis of non-conforming elements for thick plates can be formulated.Different finite element models for thick plates can be obtained by different applications of this principle. In particular,the subregion mixed variational principle for thick plates may be applied to formulating the subregion mixed finite element method for thick plates.     

Application of subregion function method in the method of weighted residuals

In this paper, a new concept of subregion function method is suggested. According to the boundary shape and the stiffness and loading conditions of the structure, the original zone of the structure is divided into some subregions, in each of which different trial functions may be adopted. Conditions of compatibilities between subregions are considered. Finally residual equations consisted of interior residuals, boundary residuals and coboundary residuals between subregions are given.A numerical example to illustrate the theory of this method is given.     

Thermoelastic-numerical hybrid analysis of holes and cracks in composites

An effective thermoelastic-numerical hybrid method is demonstrated for obtaining stress information on, and adjacent to, geometric discontinuities in orthotropic composites. This includes determining stress intensity factors. The technique involves evaluating the stress functions from measured thermoelastic data around the external boundary of a subregion containing the geometric discontinuity of interest. Knowing the stress functions, stresses throughout the subregion surrounding the geometric discontinuity, and stress intensity factors, are available.     

应用分区非线性变分原理的杂交薄壳单元

本文讨论了高次杂交壳体元在材料非线性分析中的应用，为了更精确估计单元内各部分应力的不同影响，本文应用了分区非线性变分原理推导出杂交壳元在应力增量下应用初始应力法的失衡节点力，这使得高次杂交元在非线性分析中的优点得以充分的发挥，从而大大提高了计算精度。     

边界元和激光散斑的子域杂交法

本文将计算力学的边界元法和实验力学的激光散斑法相结合用于求解受力物体的应力应变场。即用实验提供变形物体的真实边界条件,用数值方法进行求解。文中定义了虚边界的概念,并进一步提出了子域杂交法。同单纯数值计算和实验分析相比较,本文提出的方法无需构造力学模型,因而具有简单、可靠的特点,并可以更好地应用于实际问题。     

一种全耦合多相流分析的并行计算方法1)

研究了孔隙介质中热、水和汽流全耦合分析的并行计算方法.模型中采用了考虑毛细压力关系的修正有效应力概念,并考虑了相变和潜热传递.基本变量为位移、毛细压力、汽压和温度.并行程序是在国家高性能计算中心(北京)的曙光1000A上借助PVM(Parallel Virtual Machine)软件系统实现的,考题显示出较高的并行加速比和效率.     

一种全耦合多相流分析的并行计算方法

研究了孔隙介质中热、水和汽流全耦合分析的并行计算方法．模型中采用了考虑毛细压力关系的修正有效应力概念,并考虑了相变和潜热传递．基本变量为位移、毛细压力、汽压和温度．并行程序是在国家高性能计算中心（北京）的曙光１０００Ａ上借助ＰＶＭ（ＰａｒａｌｅｌＶｉｒｔｕａｌＭａｃｈｉｎｅ）软件系统实现的,考题显示出较高的并行加速比和效率     

一种新的并行自适应网格有限元算法

给出了一种新的适用于流体力学问题的并行自适应有限元算法。首先，基于初始稀网格上获得的事后误差估算值，应用反复谱对剖分方法对初网格进行划分，使各子域上总体误差近似相等，从而解决并行自适应计算中的负载平衡问题。然后在各处理器上独立地求解整体问题，并进行指定子域上的网格自适应处理。最后将各子域上的自适应网格组合成一个整体网格，应用基于粘接元技术的区域分裂法在该网格上获得最终解。文末给出了数值实验结果。     

变形测量中的数字散斑相关搜索方法

本文用仿射变换阐述了数字散斑相关方法的基本原理,通过分析散斑位移及其导数对物体变形前后散斑图的相关性的影响,对相关算法作了简化,提出了相关搜索方法.典型的实验证实了该方法的可行性,同时就散斑颗粒尺寸、子区大小对相关识别的影响等问题进行了讨论,初步给出了相关计算的有关最佳参数.     

Hybrid moiré-numerical stress analysis around cutouts in loaded composites

A hybrid experimental-numerical method is presented for evaluating the stresses around holes or notches in orthotropic composites. Moiré-measured displacements and hybrid finite elements are employed. The geometric discontinuity of interest is surrounded by a hybrid element, which is a subregion within the physical structure. Measured displacements provide input information at nodal locations on the external boundary of the hybrid element. Little experimental data are needed, and the approach is accurate and effective. The method is demonstrated for a uniaxially loaded orthotropic laminate containing a central circular hole.     

Application of a new fast multipole BEM for simulation of 2D elastic solid with large number of inclusions

A fast multipole method (FMM) is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems. In this paper, a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach. Generalized minimum residual method (GMRES) is used as an iterative solver to solve the equation system formed by BEM iteratively. The numerical results show that the scheme presented is applicable to certain large scale problems. The project supported by the National Nature Science Foundation of China (10172053) and the Ministry of Education     

近场动力学与有限元的混合建模方法

综述了近场动力学与有限元混合建模方法的研究进展,阐明了各种混合建模方法的基本原理与特点,并重点介绍本课题组在近场动力学与有限元方法混合建模方面的研究工作。现有近场动力学与有限元混合建模方法包括位移协调约束、力耦合、混合函数方法以及子模型方法等,除子模型方法外,都可归结为并行式多尺度分析方法,其基本思想是将计算结构划分为近场动力学子域、有限元子域以及两者的交界区域(或重叠区域、或界面单元、或过渡区域)。子模型方法可归结为显-显分析方法,先采用显式有限元进行整体分析,后采用近场动力学方法对重点区域进行分析。混合建模方法需要着重提高交界区域的计算精度,并且消除虚假力和虚假应力波问题。提出了通过力耦合的近场动力学与有限元混合建模的隐式分析方法,该方法不再设置重叠区,通过杆单元连接近场动力学子域与有限元子域,其中界面上的有限元结点不仅与其所在单元的其他结点发生作用,还通过杆单元与以其为圆心、一定半径的圆域内的其他物质点相互作用。研究表明,本文提出的混合模型和求解方法既能有效解决裂纹扩展等不连续问题,又可提高计算效率,为工程结构破坏问题的计算分析提供一种有效方法。     

《余能理论》引领中国变分原理的研究

正今年是钱令希院士诞辰100周年,带着崇敬的心情我们缅怀先生的一生。作为一名杰出的科学家,除了在很多研究工作中取得优秀的成果,钱令希先生的战略眼光更值得我们学习。1950年钱令希先生在中国科学杂志发表《余能理论》[1]。论文中钱令希先生引用了Westergaard 1941年关于余能原理的论文,特别引用了Westergaard的观点,认为余能方法没有受到与其价     

A nonconforming spectral element ocean model

A nonconforming spectral element ocean model, which allows a combination of higher‐ and lower‐order elements in a single formulation, is presented. The choice between the order of interpolating polynomials and the number of elements can be adjusted locally in a subregion of a domain, based on the geometric and dynamic properties of a solution. High‐order elements are applied in regions with smooth properties and achieve high‐order convergence rates. In the regions where smoothness of the solution is limited and/or geometric requirements are complex, low‐order elements are used. This paper presents a nonconforming spectral element method based on mortar elements. Convergence of the method is analyzed using several elliptic and hyperbolic test problems in two and three dimensions. To test the method, a study of wave propagation through a nonconforming interface for two problems in a realistic geometry is also presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Analysis of a plate containing an elliptic inclusion with eigencurvatures

Summary An infinite plate containing an elliptic subregion in which a uniform eigencurvature is prescribed is analyzed. The problem is formulated by using the classical plate theory. Employing the Maysel's relation, an integral-type solution to the equilibrium equation is expressed in terms of the eigencurvature. Closed-form solutions of the displacement and corresponding resultant moment are obtained for interior points as well as for exterior points of the ellipse. An infinite plate containing an elliptic inhomogeneity in which a uniform eigencurvature is prescribed is also considered. The disturbance of the displacement and corresponding resultant moment due to the inhomogeneity is determined by the equivalent eigencurvature method. Solutions of a circular finite plate with uniform eigencurvature in a circular zone are also obtained analytically. Received 30 September 1997; accepted for publication 3 February 1998     

单纤维压出实验模型的力学分析

单纤维压出实验是一种细观实验方法,用于测量复合材料的界面强度。本文采用子域法处理多域问题,利用轴对称边界元程序,对单纤维压出实验模型的应力传递进行了分析,并与常用的剪切滞后理论的分析结果进行了比较,发现在大部分纤维埋置区域,两种分析吻合很好,在纤维与基体的界面端部,边界元的分析结果显示界面应力在该区域有奇异现象,而剪滞理论则无法反映应力奇异现象。应力奇异现象的存在使得我们对该实验的界面强度判据需要     

A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems

Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multi-body systems involving impact should consider the local plastic deformation and the strict requirements of the spa-tial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlin-ear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.     

On patched variational principles in elasticity

In this paper we show how to use a combination of variational principles, each for a given subregion of the underlying region of space, so as to best utilize the chief benefits of the individual principles.     

斜波压缩实验数据的正向Lagrange处理方法研究

提出了一种联合使用Lagrange方法和转换函数方法来处理斜波压缩实验数据的新途径，和传统的数据处理方法相比，该方法更适合处理材料的复杂力学响应并具有较好的精度，同时该方法使用过程中对样品材料参数的初猜值精度要求更低。分析了转换函数方法的可靠性和健壮性，讨论了转换函数和Lagrange方法联合在斜波压缩强度实验数据处理中的应用，获得了可靠的结果。     

基于可靠性映射函数的结构优化Structural optimization based on reliability mapping functions

基于可靠性分析理论,构建可靠性映射函数,将基于可靠性的结构优化由双层优化转化为单层优化,提高优化效率,解决基于可靠性结构优化的计算量大、不利用于工程应用的问题。可靠性映射函数具有明确理论依据,能够确保将其应用到基于可靠性的结构优化是可行的。为提高失效概率求解精度,以设计点为基础,提出一种改进响应面方法,并将其用于可靠性映射函数的求解。算例表明,该方法具有较好计算精度,功能函数评估次数明显少于其他方法,计算效率高,能够获得满意的优化结果。